Open string models with Scherk-Schwarz SUSY breaking

We apply the well-known Scherk-Schwarz supersymmetry breaking mechanism in an open string context. We construct a new Z3 × Z′3 model, containing only D9branes, and rederive from a more geometric perspective the known Z′6 ×Z′2 model, containing D9, D5 and D5 branes. We show recent results about the study of quantum instability of these models. In the last years great efforts have been devoted to studying a way to embed the well-established knowledges about the Standard Model (SM) in a more fundamental microscopic theory. String theory is one of the most promising candidates along this path, but we do not have a complete solution to the problem yet. In this pattern supersymmetry (SUSY) plays a crucial role, for example explaining how the the hierarchy problem can be solved, but also stabilizing the various string models one can build. It is also clear that a phenomenologically appealing string model must contain a mechanism that breaks SUSY at a suitable scale (TeV), and this make things difficult, because it is extremely hard to build truly stable non-SUSY vacua in string theory. To this purpose we have taken into account the so-called Scherk-Schwarz (SS) symmetrybreaking mechanism [1], applicable on theories with compact extra dimensions. As described in the next section, it consists in suitably twisting the periodicity conditions of each field along some compact directions. In this way, one obtains a non-local, perturbative and calculable symmetry breaking mechanism. String models of this type can be constructed by deforming supersymmetric orbifold models [2]; a variety of four-dimensional (4D) closed string models, mainly based on Z2 orbifolds, have been constructed in this way [3]. More in general, SS symmetry breaking can be achieved through freely-acting orbifold projections [4]. This fact has been recently exploited in [5] to construct a novel class of closed string examples, including a model based on a Z3 orbifold. Unfortunately, a low compactification scale is quite unnatural for closed string models, where the fundamental string scale Ms is tied to the Planck one, and can be achieved only in very specific situations [7] (see also [8]). The situation is different for open strings, where Ms can be very low [9], and interesting open string models with SS SUSY breaking have been derived in [10, 11, 12]. Recently, the SS mechanism has been the object of renewed interest also from a more phenomenological “bottom-up” viewpoint, where it has been used in combination with orbifold projections to construct realistic 5D non-SUSY extensions of the SM [13, 14]. We will describe the general ideas proposed in [5] and build chiral IIB orientifold models with SS supersymmetry breaking. The most appealing common feature of these models is that they are tachyon-free for a suitable choice of the compactification moduli, so that instabilities, at least at the classical level, are still avoided. Recently new studies [6] have been performed to analyze the quantum stability more deeply, in particular the potential for the crucial moduli, which is flat at tree level, have been computed at one loop, showing a good behavior, at least for the model based on the Z2 orbifold. 1394 Parallel Sessions 1 The Scherk-Schwarz mechanism in string theory The Scherk-Schwarz mechanism was introduced in models where some compact extra dimension is present. Given a symmetric theory under a group G it is possible to break the symmetry by fixing different boundary conditions for fields in the same multiplet. If we consider a SUSY theory with fields φF defined on the compact dimension x ∼ x + 2πR, where F labels the fermionic or bosonic nature of each field, the procedure of SUSY breaking is encoded in the twisted boundary conditions φF (x+ 2πR) = g(F )φF (x), (1) where g(F ) is, for example, a phase that takes different values for bosons and fermions. In a compact formalism, introducing P as a translation along the compact dimension,